Unlike chatbots, physical AI must act while the world keeps evolving. Therefore, the inter-chunk pause of synchronous executors are fatal for dynamic tasks regardless of how fast the inference is. Asynchronous execution -- thinking while acting -- is therefore a structural requirement, and real-time chunking (RTC) makes it viable by recasting chunk transitions as inpainting: freezing committed actions and consistently generating the remainder. However, RTC with flow-matching policy is structurally suboptimal: its inpainting comes from inference-time corrections rather than the base policy, yielding little pre-training benefit, specific fine-tuning, heuristic guidance, and extra computation that inflates the latency. In this work, we observe that discrete diffusion policies, which generate actions by iteratively unmasking, are natural asynchronous executors that resolve all limitations at once: they are fine-tuning free since inpainting is their native operation, while early stopping further provides adaptive guidance and reduces inference cost. We propose DiscreteRTC, which replaces external corrections with native unmasking, and show on dynamic simulated benchmarks and real-world dynamic manipulation tasks that it achieves higher success rates than continuous RTC and other baselines. In summary, DiscreteRTC is simpler to implement with 0 lines of additional code to enable async inpainting, faster at inference with only ~0.7 computation compared with generating actions from scratch, and better at execution with 65% higher success rate in real-world hockey defend task compared with flow-matching RTC, and 30% higher compared with training-time flow-matching RTC. More visualizations are on https://outsider86.github.io/DiscreteRTCSite/.